divide 28 cans of soda into two groups so the ratio is 3 and 4

Answer:

3(x - 4)(x + 4)

Step-by-step explanation:

[tex]3 {x}^{2} - 48 \\ = 3( {x}^{2} - 16) \\ = 3( {x}^{2} - {4}^{2} ) \\ = 3(x - 4)(x + 4)[/tex]

5 equilateral triangles.

Hope this helps.

Answer:

-7

Step-by-step explanation:

-5 + (-2)

You are adding two negative numbers, -5 and -2.

Find their absolute values: 5 and 2.

Add the absolute values: 5 + 2 = 7

The answer is negative: -7

-5 + (-2) = -7

Answer:

[tex]P(M) = \frac{1}{3}[/tex]

The game is not a fair game

Step-by-step explanation:

We start by listing out the sample space

Number Cube 1: {1,2,3,4,5,6}

Number Cube 2: {1,2,3,4,5,6}

Sample Space (S) of the sum of the 2 cubes;

[tex]S = \{2,3,4,5,6,7,3,4,5,6,7,8,4,5,6,7,8,9,5,6,7,8,9,10,6,7,8,9,10,11,7,8,9,10,11,12\}[/tex]

[tex]n(S) = 36[/tex]

Next, is to list out all multiples of 3; Represent this with M

[tex]M = \{3,6,3,6,6,9,6,9,6,9,9,12\}[/tex]

[tex]n(M) = 12[/tex]

Your probability of winning is the probability of M and is calculated as thus;

[tex]P(M) = \frac{n(M)}{n(S)}[/tex]

[tex]P(M) = \frac{12}{36}[/tex]

[tex]P(M) = \frac{1}{3}[/tex]

The probability of Kyle winning, P(K) = 1 - P(M)

[tex]P(K) = 1 - \frac{1}{3}[/tex]

[tex]P(K) = \frac{2}{3}[/tex]

The game is not a fair game because;

The probability of you winning and the probability of Kyle winning are not equal;

Answer:

[tex]x=-9[/tex]

Step-by-step explanation:

[tex]5x+12=-33[/tex]

Subtract 12 from both sides. The left side cancels:

[tex](5x+12)-12=(-33)-12\\5x=-45[/tex]

Divide both sides by 5. The left side cancels:

[tex](5x)/5=(-45)/5\\x=-9[/tex]

The value of x is -9.

Answer:

1) The equation is given in factored form

2) The key characteristics of the parabola are;

a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are (1/2, 0) and (-6, 0)

c. The y intercept is (0, -6)

d. The vertex point is (-2.75, -21.125)

Step-by-step explanation:

The given equation is f(x) = (2·x -1)(x + 6)

Therefore the equation is given in factored form

The key characteristic of the parabola revealed from the form f(x) = (2·x -1)(x + 6) are;

1) Writing the parabola in the intercept form, a(x - p)(x -q) we have;

f(x) = (2·x -1)(x + 6) = 2·(x - 1/2)(x + 6)

p = 1/2, q = -6

Therefore;

Given that a is positive the parabola is concave upwards

2) a. The parabola has 2 real roots and extends to infinity on both sides

b. The x-intercepts of the parabola are p and q which are (1/2, 0) and (-6, 0)

c. The y intercept is a·(-p)·(-q) = 2×(-1/2)×6 = -6

The y intercept is (0, -6)

d. Expanding we get;

f(x) = 2·x² + 11·x - 6

From the

The vertex is h = -b/(2·a) = -11/(2×2) = -2.75

h(2.75) = 2×(-2.75)² + 11×(-2.75) - 6 = -21.125

Therefore, the function is symmetrical about the vertex point (-2.75, -21.125)

Answer:

Option B.

Step-by-step explanation:

We need to find the range of numbers is most appropriate for the y-axis scale and interval on a graph for given table.

From the given table it is clear that the minimum value of y is 10 and the maximum value of y is 34.

It means 10 and 34 must be included in the Range.

In option C and D 34 in not included in the range, so these options are incorrect.

In option A, 10 is the minimum value of range and interval of 10 is not possible for the range 10-35, because it contains only multiple of 10 on the y-axis. So, this option is incorrect.

In option B, both 10 and 34 are included and interval of 5 is possible for range 0-35.

Therefore, the correct option is B.

Answer:

Step-by-step explanation:

This problem bothers on the mensuration of flat shapes, circles.

given that  the members of the community used  rope as outline for the circular shape mural.

we can tell that the perimeter of the mural is same as the perimeter of the rope.

Hence the length of rope used is same as the perimeter of the circular mural.

we know that the perimeter of a circle is given as

[tex]C=2\pi r\\\\[/tex]

substituting radius r= 11 yards

we have

[tex]C= 2*3.142*11\\\\C= 69.124 yards[/tex]

Answer:

B

Step-by-step explanation:

So we have the equation:

[tex]12x+18=4(5x-3)[/tex]

Distribute the right:

[tex]12x+18=20x-12[/tex]

Add 12 to both sides:

[tex]12x+30=20x[/tex]

Subtract 12 from both sides:

[tex]30=8x[/tex]

Divide both sides by 8:

[tex]x=30/8[/tex]

Reduce:

[tex]x=15/4[/tex]

Put into mixed fractions:

[tex]x=12/4+3/4=3\text{ } 3/4[/tex]

Our answer is B :)

Answer:

[tex]B. \:3\frac{3}{4}[/tex]

Step-by-step explanation:

[tex]12x+18=4(5x-3)\\\\\mathrm{Expand\:}4\left(5x-3\right):\quad 20x-12\\12x+18=20x-12\\\\\mathrm{Subtract\:}18\mathrm{\:from\:both\:sides}\\12x+18-18=20x-12-18\\\\Simplify\\12x=20x-30\\\\\mathrm{Subtract\:}20x\mathrm{\:from\:both\:sides}\\12x-20x=20x-30-20x\\\\Simplify\\-8x=-30\\\\\mathrm{Divide\:both\:sides\:by\:}-8\\\frac{-8x}{-8}=\frac{-30}{-8}\\\\Simplify\\x=\frac{15}{4}\\\\15\div 4 = 3remainder3\\\\=3\frac{3}{4}[/tex]

Answer: B

Step-by-step explanation:

The end behavior of f(x) is that both ends go down. The correct answer is B.

Function is a type of relation, or rule, that maps one input to specific single output.

In mathematics, a function is an expression, rule, or law that describes the relationship between one variable (the independent variable) and another variable (the dependent variable) (the dependent variable). In mathematics and the physical sciences, functions are indispensable for formulating physical relationships.

Linear function is a function whose graph is a straight line

We are given that;

f(x) = -3x^4+2x^2-x

Now,

we can find the end behavior of f(x) = -3x^4 + 2x^2 - x:

The degree of f(x) is 4, which is even. Therefore, both ends of the graph will either go up or go down.

The leading coefficient of f(x) is -3, which is negative. Therefore, the right end of the graph will go down.

Since both ends have to go in the same direction, and the right end goes down, then the left end must also go down.

Therefore, by the given function the answer will be both ends go down

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Answer:

x = m - a/b + k

Step-by-step explanation:

m = x + (a / b) - k ​

switch sides

x + a/b - k = m

subtract a/b - k from both sides

a + a/b - k - (a/b - k) = m - (a/b - k)

therefore,

x = m - a/b + k

Explanation:

You basically plug in x = 20, which is the same as saying "replace x with 20". Then you perform arithmetic to simplify each expression. Both simplify to 90, so angle 1 and angle 2 are the same measure. These angles are alternate interior angles, so we'll use the converse alternate interior angle theorem to conclude the lines are parallel.

Note: the alternate interior angle theorem says that if we have parallel lines, then the alternate interior angles are congruent. So the converse goes in reverse of this.

Answer:

11521 km

Step-by-step explanation:

The computation is given below:

But prior to reaching the final solution first the following calculations need to be computed

Angle between the Galapagos and Nauru is

= 90.30° + 166.56°

= 256.86°

As we know that the total of angles is  360 degrees

Now the major arc and the minor arc is

= 360° -  256.86°

= 103.14°

So,  the angles between galapagos islands is

= 180°  - 90.30°

= 89.70°

And, angles between the naura island is

= 180°  - 166.56°

= 13.44°

Now the sum of this two island is

= 89.70°  + 13.44°

= 103.14°

Therefore The length is

[tex]= \frac{\pi r}{180^{\circ}} \times \theta \\\\ = \frac{6,400 \pi}{180^{\circ}} \times 103.14^{\circ}[/tex]

= 11521 km

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Answer : (B) [tex]100,000,000 + 20,000,000 + 4,000,000 + 700,000 + 50,000 = 124,750,000[/tex]

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Have a great day/night!

❀*May*❀

Answer:

B.

Step-by-step explanation:

124,750,000=100,000,000

20,000,000

4,000,000

700,000

+50,000

Hope this helps ;) ❤❤❤

Answer:

(40+2)+(6x4)

Step-by-step explanation:

Forty plus two is forty-two, and six times four is twenty-four. So, add them together and you'll get the same answer! Hope this helps!

Answer:

t = (q - r) / rs

Step-by-step explanation:

Right now you have q=rst+r so if you want to find t you must move the variables around. Like this:

q=rst+r (or r+rst)

so so get rid of the r first

like this: (q-r)=rst

divide by rs to find t

so t=(q-r)/rs

Answer: 1.64

Step-by-step explanation: You need to do 6.56/4 which is 1.64

Answer:

[tex]\Huge \boxed{4^{16} }[/tex]

Step-by-step explanation:

[tex]16^8[/tex]

Rewrite 16 with base 4.

16 is also written as 4².

[tex](4^2)^8[/tex]

We can apply an exponent rule :

[tex](a^b)^c=a^{bc}[/tex]

Multiply the exponents.

[tex]4^{2 \times 8}[/tex]

[tex]4^{16}[/tex]

Answer:

Last year there were 1070 students.

Step-by-step explanation:

Since 856 students represent a 20% drop from last year's number of students, then 856 students is 80% of last year's number.

80% of x = 856

0.8x = 856

x = 856/0.8

x = 1070

Answer: Last year there were 1070 students.

Answer:

1070

Step-by-step explanation:

p = previous years populations

p - p 20% = 856

p - .20*p = 856

Combine like terms

.80p = 856

Divide each side by .8

.80p/.8 - 856/.8

p =1070

Answer:

C

Step-by-step explanation:

The difference between 30 and 15 is 15

then multiply the 15 % with 400

and you will get the value 60 which is the answer you want

Answer:

C. 60

Step-by-step explanation:

To find the difference between them, we must:

1. Find the amount of the percentage.

(Percent (%) is always over 100)

30% of 400 = 30/100 × 400/1

=12,000/100 = 120

So 30% of 400 is 120.

15% of 400 = 15/100 × 400

=6,000/100 = 60

So 15% of 400 is 60.

2. Then subtract the amount of the percentages to find their difference.

120 - 60= 60

So the difference between 120 and 60 is 60.

I hope this helps! I'm sorry if it's wrong or too complicated.

Answer:

8.75

Step-by-step explanation:

because it had increase in percent is about 70 % which is 70% do the same to 5.25 which is 8.75

Answer:

$8.75

Step-by-step explanation:

We can use ratios to solve

150 vitamins       250 vitamins

------------------ = ------------------

$5.25                     $x

Using cross products

150x = 250 (5.25)

150x =1312.5

Divide each side by 150

x =1312.5/150

x =8.75

Answer:

Width = 12 foot

Length = 24 foot

Step-by-step explanation:

Let

Width=x

Length=2x

Area = 288 square feet

Area of the garage = Length × width

288 = 2x * x

288= 2x^2

Divide both sides by 2

288 / 2 = x^2

144= x^2

Find the square root of both sides

√144 = √x^2

12 = x

Therefore,

x=12

The dimensions will be:

Width = x

= 12

Length = 2x

=2(12)

=24

Width = 12 foot

Length = 24 foot

Volume of cube = side length^3

Volume = 14^3

Volume = 2,744 cubic meters

Answer:

v=x^3

14^3=2744

.....

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The simplest method to find a rational number between two rational numbers x and y is to divide their sum by 2.

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Answer:

1

Step-by-step explanation:

Given

[tex]\frac{14x}{10y}[/tex] ← substitute x = 5 and y = 7 into the expression

= [tex]\frac{14(5)}{10(7)}[/tex]

= [tex]\frac{70}{70}[/tex]

= 1

Answer:

c 58

Step-by-step explanation:

Answer:

62

Step-by-step explanation:

Add all of them and it’s 180

Answer:

No opposite

Step-by-step explanation:

Zero has no opposite because it is neither positive or negative.

The value of the number that is the opposite of 0​ is 0

From the question, we have the following parameters that can be used in our computation:

Number = 0

By definition:

The number that is the opposite of a number x is -x

using the above as a guide, we have the following:

Opposite = -0

Evaluate

Opposite = 0

Hence, the number that is the opposite of 0​ is 0

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Answer:

The value of k is 46°.

Step-by-step explanation:

Given that when 2 angles add up together, they will form 75°.

So in order to find the value of k, you have to subtract 29° from 75° :

[tex]k + 29 = 75[/tex]

[tex]k = 75 - 29[/tex]

[tex]k = 46[/tex]

Answer:

46 degrees.

Step-by-step explanation:

The whole angle is 75 degrees. So you subtract the given value with the total angle. 75-29=46 degrees.

First replace x with -2 in the g(x) equation and solve:

G(x) = x + 4 = -2 + 4 = 2

Now replace x in the f(x) equation with the solution of g(x).

F(x) = 1-3(2) = 1-6 = -5

Fg(-2) = -5